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Chapter 3
Members in Bending

## Excerpt

Many components in pressurized equipment operating in the creep range consist of beams and flat plates in bending. These include piping components, internal catalyst supports, nozzle covers, and tubesheets. In this chapter, the characteristics of beams in bending are studied first, followed by an evaluation of flat circular plates in bending.

The characteristics of beams in bending operating in the creep range have been studied by many engineers and researchers. Theoretically, the analysis is based on the following Norton's relationship correlating stress and strain rate in the creep regime as discussed in Chapters 1 and 2 and as given by

$dε∕dT=k′σn$
where k = constant n = creep exponent, which is a function of material property and temperature dε∕dT = strain rate σ = stress

This equation, however, is impractical to use for most problems encountered by the engineer as discussed in Section 2.1. A simpler method, referred to as the stationary stress or the elastic analog method, is normally used to solve beam bending problems and is given by

$ε=K′σn$

• 3.1 Introduction
• 3.2 Bending of Beams
• 3.2.1 Rectangular Cross-Sections
• 3.2.2 Circular Cross-Sections
• 3.3 Shape Factors
• 3.3.1 Rectangular Cross-Sections
• 3.3.2 Circular Cross-Sections
• 3.4 Deflection of Beams
• 3.5 Piping Analysis — ANSI 31.1 and 31.3
• 3.5.1 Introduction
• 3.5.2 Design Categories and Allowable Stresses
• 3.5.3 Creep Effects
• 3.6 Stress Analysis
• 3.6.1 Commercial Programs
• 3.7 Reference Stress Method
• 3.8 Circular Plates
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